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PSAT Math : Operations with Fractions

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Example Questions

Example Question #13 : Operations With Fractions

Solve $\frac{3}{7}+\frac{5}{8}-\frac{1}{2}$ $\displaystyle \frac{3}{7}+\frac{5}{8}-\frac{1}{2}$.

Possible Answers:

$\frac{33}{56}$ $\displaystyle \frac{33}{56}$

$\frac{31}{56}$ $\displaystyle \frac{31}{56}$

$\frac{5}{7}$ $\displaystyle \frac{5}{7}$

$\frac{7}{8}$ $\displaystyle \frac{7}{8}$

Correct answer:

$\frac{31}{56}$ $\displaystyle \frac{31}{56}$

Explanation:

Finding the common denominator yields $\frac{24}{56}+\frac{35}{56}-\frac{28}{56}$ $\displaystyle \frac{24}{56}+\frac{35}{56}-\frac{28}{56}$. We can then evaluate leaving $\frac{31}{56}$ $\displaystyle \frac{31}{56}$.

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Example Question #31 : Operations With Fractions

What is the solution, reduced to its simplest form, for $x = \frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}}$ $\displaystyle x = \frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}}$ ?

Possible Answers:

$x =2$ $\displaystyle x =2$

$x = \frac{7}{15}$ $\displaystyle x = \frac{7}{15}$

$x = \frac{115}{45}$ $\displaystyle x = \frac{115}{45}$

$x = \frac{75}{45}$ $\displaystyle x = \frac{75}{45}$

$x = \frac{5}{3}$ $\displaystyle x = \frac{5}{3}$

Correct answer:

$x = \frac{5}{3}$ $\displaystyle x = \frac{5}{3}$

Explanation:

$x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}$ $\displaystyle x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}$

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Example Question #131 : Fractions

What is the sum of $\small \frac{4}{5}$ $\displaystyle \small \frac{4}{5}$ and $\small 2 \frac{5}{6}$ $\displaystyle \small 2 \frac{5}{6}$?

Possible Answers:

$\small \frac{109}{30}$ $\displaystyle \small \frac{109}{30}$

$\small \frac{30}{109}$ $\displaystyle \small \frac{30}{109}$

$\small \frac{79}{30}$ $\displaystyle \small \frac{79}{30}$

$\small \frac{49}{109}$ $\displaystyle \small \frac{49}{109}$

$\small \frac{49}{12}$ $\displaystyle \small \frac{49}{12}$

Correct answer:

$\small \frac{109}{30}$ $\displaystyle \small \frac{109}{30}$

Explanation:

We can begin by eliminating the obviously wrong answers. We know that the sum of the two fractions will be more than 1, so the answer choices $\tiny \tiny \frac{49}{109}$ $\displaystyle \tiny \tiny \frac{49}{109}$ and $\small \frac{30}{109}$ $\displaystyle \small \frac{30}{109}$ are out. Now, let's add the two fractions:

Begin by converting $\small 2 \frac{5}{6}$ $\displaystyle \small 2 \frac{5}{6}$ to $\tiny \frac{17}{6}$ $\displaystyle \tiny \frac{17}{6}$.

Now find the common denominator of $\small \frac{4}{5}$ $\displaystyle \small \frac{4}{5}$ and $\tiny \frac{17}{6}$ $\displaystyle \tiny \frac{17}{6}$. The least common multiple of 5 and 6 is 30, so 30 is the common denominator. Now alter both fractions so that they use the common denominator:

$\tiny \small \frac{4}{5}= \frac{4*6}{5*6}=\frac{24}{30}$ $\displaystyle \tiny \small \frac{4}{5}= \frac{4*6}{5*6}=\frac{24}{30}$

$\tiny \small \frac{17}{6}=\frac{17*5}{6*5}=\frac{85}{30}$ $\displaystyle \tiny \small \frac{17}{6}=\frac{17*5}{6*5}=\frac{85}{30}$

Now we can easily add the two fractions together:

$\small \frac{24}{30}+\frac{85}{30}=\frac{109}{30}$ $\displaystyle \small \frac{24}{30}+\frac{85}{30}=\frac{109}{30}$

The answer is $\small \frac{109}{30}$ $\displaystyle \small \frac{109}{30}$.

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PSAT Math : Operations with Fractions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #13 : Operations With Fractions

Example Question #31 : Operations With Fractions

Example Question #131 : Fractions

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